With the baseball list, I didn't really take era into consideration too much: old timers were considered right alongside new timers. Old timers will be slightly penalized in this one just because the game has changed SO much (not that baseball hasn't, but it's a different degree). And I'll still be doing the greatest in all of franchise history, and then the greatest in the franchise's current iteration.
Atlanta Hawks: The greatest Hawk ever is Dominique Wilkins, with all due respect to Bob Pettit. This one's pretty close, so since Wilkins is the more current player, he gets the nod. Tough one right off the bat though.